1. What does it mean?
생축 takes 생 from 생일 and 축 from 축하. It is a compact birthday greeting used in messages, captions, and quick exchanges with people you know.
Also written or said as saengchuk
2. The nuance
A fuller 생일 축하해 or 생일 축하합니다 adds warmth or formality. The abbreviation is a greeting, unlike 생파, which refers to the party.
3. Examples
“지수야 생축! 오늘은 푹 쉬고 맛있는 거 먹어.”
Happy birthday, Jisu! Rest up and eat something good today.
“날짜 바뀌자마자 친구한테 생축 메시지를 보냈어.”
I sent my friend a happy-birthday message right after midnight.
Sources
References support the meaning and usage. Example sentences are written for NoCapWiki.